eXjX úim/2 /2b aG*A ¨ T`iB` /2b /B;`KK2b /2 "Q/2

(1)

MHvb2 7`Ā[m2MiB2HH2 /2b bvbiĚK2b HBMĀB`2b

eXRX .2 H `ûTQMb2 i2KTQ`2HH2 ¨ H `ûTQMb2 7`û[m2MiB2HH2

eXRXRX _ûTQMb2 7`û[m2MiB2HH2

MRnc IIRNc cna nN 3u3LUI3 cCLUI3 LRNja3a I a3IjCRN \nȕCI 3uCcj3 3Nja3 I 8RN,jCRN 03 jaNc83aj 0Nc I3 0RLCN3 03 HUI,3 3j I aāURNc3 j3LURa3II3 3N aā<CL3 U3aLN3Nj 0ȕnN cC<NI cCNncRŧ0IY

bRCj Iȕā\njCRN 0C{āa3NjC3II3 0n S^3aRa0a3 - τ·^d^s(t)

dt +s(t) =K·e(t) QN c3 UI,3 0Nc I3c ,RN0CjCRNc 03 ?3qCcC03Y

QN ,@3a,@3 I aāURNc3 j3LURa3II3s(t)URna nN3 3Njaā3 e(t) =cos(ω·t)·h(t)

H cRInjCRN 03 Iȕā\njCRN <āNāaI3 03 ,3jj3 ā\njCRN 0C{āa3NjC3II3 3cj -

sg(t) =G·e⁻ t τ q3,G© 0āj3aLCN3a 3N 8RN,jCRN 03c ,RN0CjCRNc CNCjCI3cY

H cRInjCRN UajC,nICěa3 3cj 03 I 8RaL3 \n3e(t)- sp(t) = A·cosω·t+B·sinωt

2N a3LUIÓNj 0Nc Iȕā\njCRN 0C{āa3NjC3II3. RN R$jC3Nj -

−A·τ·ω·sinω·t+B·τ·ω·cosω·t+A·cosω·t+B·sinωt =K·cosω·t (−A·τ·ω+B)·sinωt+ (B·τ·ω+A)·cosω·t =K·cosω·t

cRCj

B·τ·ω+A=K

−A·τ·ω+B=0 QN 0ā0nCj

sp(t) =K

1

1+τ²·ω² ·cosωt+ ^τ·ω

1+τ²·ω²sinωt

S

(2)

QN URc3ϕj3I \n3sinϕ= √ ^τ·ω

1+τ²·ω² 3jcosϕ= √ ¹ 1+τ²·ω²

sp(t) = √ ^K

1+τ²·ω²(cosϕ·cosωt+sinϕ·sinωt) sp(t) = √ ^K

1+τ²·ω²·(ω·t−ϕ) H cRInjCRN ,RLUIěj3 cȕā,aCj 0RN, -

s(t) =K·e⁻ t

τ +√ ^K

1+τ²·ω²·cos(ω·t−ϕ)

QN 3N 0ā0nCj I3 ,RLURaj3L3Nj 3N aā<CL3 U3aLN3Nj. ,ȕ3cj © 0Ca3 IRac\n3t3cj cn|cLL3Nj <aN0 sperm(t) = √ ^K

1+τ²·ω² ·cos(ω·t−ϕ) QN 3N 0ā0nCj -

ġ IȕLUICjn03 03sperm(t)- √ K 1+τ²·ω² ġ I3 0āU@c<3 © IȕRaC<CN3ϕ=−arctan(τ·ω)

eXRXkX .2 H i`Mb7Q`Kû2 /2 GTH+2 ¨ H `ûTQMb2 7`û[m2MiB2HH2

QN 0ā0nCj 03 Iȕā\njCRN 0C{āa3NjC3II3 0n Ua3LC3a Ra0a3 I 8RN,jCRN 03 jaNc83aj H(p) = ^S(p)

E(p) = ^K 1+τ·p

QN cCj \n3 I qaC$I3 03 HUI,3p3cj nN NRL$a3 ,RLUI3u3p=a+j·bY QN ,@RCcCjpCL<CNCa3 Una cRCjp= j·ωY `3LUIÓRNc p= j·ω0NcH p)Y

H(j·ω) = ^S(j·ω)

E(j·ω) = ^K 1+τ·j·ω

H(j·ω)3cj nN3 8RN,jCRN ,RLUI3u3 0RNj RN U3nj ,I,nI3a I3 LR0nI3 3j Iȕa<nL3NjY 0ȕRɵ KQ/mH2 ,

|H(j·ω)|= A(ω) = √ ^K 1+τ²·ω²

`;mK2Mi

arg(H(j·ω)) =Φ(ω) =−arctan(τ·ω) QN a3,RNNţj IȕLUICjn03 03sperm(t)^3jϕY

QN U3nj 0RN,. 0Ca3,j3L3Nj © UajCa 03 I 8RN,jCRN 03 jaNc83aj. a3jaRnq3a I3c ,a,jāaCcjC\n3c 03 I aāA URNc3 3N aā<CL3 U3aLN3Nj 0ȕnN cwcjěL3 cRIIC,Cjā q3, nN3 3Njaā3 cCNncRŧ0I3Y

QN UU3II3 aāURNc3 8aā\n3NjC3II3 0ȕnN cwcjěL3 I aāURNc3 j3LURa3II3 3N aā<CL3 U3aLN3Nj 0ȕnN cwcA jěL3 ICNāCa3 cRIIC,Cjā Ua nN3 3Njaā3 cCNncRŧ0I3Y

l Hw,ā3 +@aI3L<N3ATaCc

(3)

eXkX _ûTQMb2 7`û[m2MiB2HH2

H(p) = ^N_D⁽₍_p^p⁾₎ E(p) S(p) HȕR$E3,jC8 03 IȕNIwc3 8aā\n3NjC3II3 3cj 0ȕājn0C3a I3 ,RLURaj3L3Nj 0ȕnN

cwcjěL3 © UajCa 03 c aāURNc3 © nN3 cRIIC,CjjCRN cCNncRŧ0I3 03 I 8RaL3 e(t) = A·sin(ω·t)· H(t)

q3,H(t). I 8RN,jCRN ?3qCcC03 3cj 0ā~NC3 Ua -

t ≤0 H(t) =0 t ≥0 H(t) =1 Y

QN cRIIC,Cj3 0RN,. I3 cwcjěL3 q3, nN3 3Njaā3 cCNncRŧ0I3 03 UnIcjCRNω 3j RN a3Iěq3 I aāURNc3 j3LA URa3II3 03 I cRajC3 URna ,@,nN3 03c 8aā\n3N,3cY H ~<na3 fYS Uaāc3Nj3 \n3I\n3c L3cna3cY

t c

z S

VWf =4Hz

t c

z S

V$W f =8Hz

t c

z S

V,Wf=10Hz

7ϔόЛЁζ fYSY Ģ `3I3qāc 8aā\n3NjC3Ic QN a3La\n3 cna ,3c ja,āc -

ġ I Uaāc3N,3 03 03nu yRN3c -

ġ I3 aā<CL3 jaNcCjRCa3 VI U@c3 03 0āLaa<3W d ġ I3 aā<CL3 U3aLN3Nj Rn aā<CL3 āj$IC d

ġ \n3 I3 0āU@c<3 0n aā<CL3 U3aLN3Nj q3, I3 cC<NI 0ȕ3Njaā3 n<L3Nj3 q3, I UnIcjCRN d ġ \n3 IȕLUICjn03 03 I cRajC3 qaC3 q3, I UnIcjCRNY

t c

z S

`3ja0 03 U@c3 2Njaā3

bRajC3

iaNcCjRCa3 `ā<CL3 U3aLN3Nj Ā,aj 0ȕLUICjn03

7ϔόЛЁζ fYlY Ģ `āURNc3 8aā\n3NjC3II3

Hw,ā3 +@aI3L<N3ATaCc k

(4)

QN ,RNcjj3 \n3 I aāURNc3 VURna I3 aā<CL3 U3aLN3NjW IȕIIna3 0ȕnN3 cCNncRŧ03 03 LćL3 UnIcjCRN LCc 3N a3ja0 Ua aUURaj n cC<NI 0ȕ3Njaā3Y

TRna ,a,jāaCc3a I aāURNc3 8aā\n3NjC3II3 0n cwcjěL3 CI 3cj URccC$I3 0ȕājn0C3a IȕāqRInjCRN URna I3 aā<CL3 U3aLN3Nj 03 I qaCjCRN 0ȕLUICjn03 3j 0n 0āU@c<3 3Nja3 I3 cC<NI 0ȕ3Njaā3 3j I cRajC3 V~<na3 fYl WY

TRna nN cwcjěL3 ICNāCa3. NRnc cqRNc \n3 I cRajC3 3N aā<CL3 U3aLN3Nj 3cj 03 LćL3 Njna3 \n3 Iȕ3Njaā3. Iȕā\njCRN j3LURa3II3 0n aā<CL3 U3aLN3Nj 03 I cRajC3 c3 L3j 0RN, cRnc I 8RaL3 -

s(t) =A0·A(ω)·sin(ω·t+Φ(ω)) q3,

ġ A(ω)- I3 aUURaj 03c LUICjn03c 0n cC<NI U3aLN3Nj. 3Nja3 Iȕ3Njaā3 3j I cRajC3 d ġ Φ(ω)- I3 0āU@c<3 3Nja3 Iȕ3Njaā3 3j I cRajC3 d

,3c 03nu 8RN,jCRNc cRNj 03c 8RN,jCRNc 03 I UnIcjCRNωY eXkXRX 6QM+iBQM /2 i`Mb72`i +QKTH2t2

H(p) E(p) S(p) bRCj nN cwcjěL3 ICNāCa3 ,RNjCNn CNqaCNj VbH+BW ,RNNn Ua c 8RN,jCRN 03

jaNc83aj 0Nc I3 0RLCN3 03 HUI,3. I 8RN,jCRN 03 jaNc83aj 0n cwcjěL3 3cj Ua 0ā~NCjCRN -H(p) = ^S(p)

E(p)

QN NRj3 2VUW 3j bVUW I3c jaNc8RaLā3c 0Nc I3 0RLCN3 03 HUI,3 03c 8RN,A jCRNc j3LURa3II3c 3VjW 3j cVjW 3j ?VUW I 8RN,jCRN 03 jaNc83ajY

QN UU3II3 8RN,jCRN 03 jaNc83aj ,RLUI3u3 VRn jaNcLCjjN,3 CcR,@aRN3W I 8RN,jCRN R$j3Nn3 3N a3LA UIÓNj I qaC$I3 03 HUI,3 pUa I3 j3aL3 CL<CNCa3 Unaj·ω-

H(j·ω) = ^S(j·ω) E(j·ω)

+3jj3 8RN,jCRN 3cj nN3 8RN,jCRN ,RLUI3u3 03 I qaC$I3ω. ,RLL3 jRnj3 8RN,jCRN ,RLUI3u3. URna 3N aāICc3a Iȕājn03. RN U3nj cRCj cȕCNjāa3cc3a -

ġ © I UajC3 aā3II3 3j © I UajC3 CL<CNCa3.

ġ n LR0nI3 3j © Iȕa<nL3NjY eXkXkX GB2mt /2 i`Mb72`i

QN UU3II3 IC3nu 03 jaNc83aj. I3 ja,ā 03c 0C{āa3Nj3c a3Uaāc3NjjCRNc <aU@C\n3c 03 I 8RN,jCRN 03 jaNc83ajH(j·ω)Y

b3nI3 I aāUaāc3NjjCRN <aU@C\n3 03c IC3nu 03 jaNc83aj Ua I3c 0C<aLL3c 03 #Q/2 3cj n UaRA

<aLL3Y

¨ UajCa 03 ,3jj3 a3Uaāc3NjjCRN <aU@C\n3. NRnc URnaaRNc ,a,jāaCc3a I3 ,RLURaj3L3Nj <IR$I 0n cwcjěL3 ICNāCa3 VUcc3 $c. Ucc3 $N03. aācRNN,3. ĞWY

: Hw,ā3 +@aI3L<N3ATaCc

(5)

**eXjX úim/2 /2b aG*A ¨ T`iB` /2b /B;`KK2b /2 "Q/2**

eXjXRX .B;`KK2b /2 "P.1

H3c 0C<aLL3c 03 #R03 a3Uaāc3Nj3Nj V~< ]]W cāUaāL3Nj I3 LR0nI3 3j I U@c3 03 I 8RN,jCRNH(j·ω)^Y QN NRj3

ġ A(ω) =|H(j·ω)|I3 LR0nI3.

ġ Φ(ω) =arg(H(j·ω)Iȕa<nL3Nj

10⁰ 10¹ 10² 10³ 10⁴

−120

−100

−80

−60

−40

−20 0 200#

a0gc

ia,ā 3u,j

ia,ā cwLUjRjC\n3

ω3N a0gc A ā,@3II3 IR<aCj@LC\n3

10⁰ 10¹ 10² 10³ 10⁴

−270

−240

−210

−180

−150

−120

−90

−60

−30 0

◦

a0gc

ia,ā 3u,j

ia,ā cwLUjRjC\n3

7ϔόЛЁζ fYkY Ģ /C<aLL3c 03 #R03 TRna ,3c 0C<aLL3c -

ġ Iȕ$c,Ccc3 3cj nN3 ā,@3II3 IR<aCj@LC\n3 03 I UnIcjCRN -log₁₀(ω)d ġ IȕRa0RNNā3 0n 0C<aLL3 0ȕLUICjn03 3cj <a0nā3 3N 0ā,C$3Ic VdBW -

AdB(ω) =20 log₁₀(|H(jω)|), ġ IȕRa0RNNā3 0n 0C<aLL3 03 U@c3. 3N 03<aā Rn a0CNY

QN cnU3aURc3 3N <āNāaI n ja,ā 3u,j I3 ja,ā cwLUjRjC\n3. ,3InCA,C 3cj cRnq3Nj cn|cNj URna NA Iwc3a I 8RN,jCRNY H ~<na3 fYk LRNja3 nN 3u3LUI3 03 ja,ā 03c 0C<aLL3c 03 #R03Y

eXjXkX S`QT`Bûiûb /2b /B;`KK2b /2 "Q/2

bRCj nN cwcjěL3 ICNāCa3 0ā,aCj Ua I3 c,@āL $IR, ,CA03ccRncY G(p) =G1(p)·G2(p)

bRCj 3N ,RLUI3u3

G(j·ω) =G1(j·ω)·G2(j·ω)

G1(p) G2(p) X(p) Y(p) Z(p)

Hw,ā3 +@aI3L<N3ATaCc 9

(6)

0ȕRɵ I3 LR0nI3 aā3I

|G(j·ω)|=|G1(j·ω)| · |G2(j·ω)|

3j I3 LR0nI3 3NdB

G_dB(ω) =20 log(|G1(j·ω)|) +20 log(|G2(j·ω)|)

= G1dB(ω) +G2dB(ω)

UnCc Iȕa<nL3Nj

arg(G(j·ω)) =arg(G1(j·ω)) +arg(G2(j·ω))

;aU@C\n3L3Nj. CI cn|j 0RN, 0ȕERnj3a I3c 0C<aLL3c 03 #R03 03c 8RN,jCRNcG1(p)3jG2(p)nccC

$C3N URna I3 0C<aLL3 0ȕLUICjn03 \n3 URna I3 0C<aLL3 03c U@c3c URna R$j3NCa I3c 0C<aLL3c 03G(p) =G1(p)·G2(p)Y

eX9X avbiĕK2 /m T`2KB2` Q`/`2

mN cwcjěL3 0n Ua3LC3a Ra0a3 3cj 0ā,aCj Ua nN3 ā\njCRN 0C{āa3NjC3II3 ICNāCa3 © ,R3|,C3Njc ,RNcjNjc 0n Ua3LC3a Ra0a3 -

τds(t)

dt +s(t) =K.e(t) q3, τ- ,RNcjNj3 03 j3LUc K- <CN cjjC\n3

QN URc3 -e(t)−→^L E(p)3js(t)−→^L S(p)Y QN c3 UI,3 0Nc I3c ,RN0CjCRNc 03 ?3qCcC03Y 7RN,jCRN 03 jaNc83aj 3j c,@āL $IR, 0ȕnN cwcjěL3 0n Ua3LC3a Ra0a3 -

H(p) = ^S(p)

E(p) = ^K 1+τ·p

K 1+τ·p

2VUW bVUW

eX9XRX _2T`ûb2MiiBQM 7`û[m2MiB2HH2

QN R$jC3Nj I 8RN,jCRN 03 jaNc83aj ,RLUI3u3 3N URcNjp =j·ω- H(j·ω) = ^K

1+τ·j·ω 3j RN 3N 0ā0nCj -

ġ I UajC3 aā3II3 -

Re(j·ω) = ^K 1+τ²·ω²

ġ I UajC3 CL<CNCa3 -

Im(j·ω) = −K·τ·ω 1+τ²·ω²

ġ I3 LR0nI3 -

A(ω) = √ ^K 1+τ²·ω²

ġ Iȕa<nL3Nj -

Φ(ω) =−arctan(τ·ω) ġ I3 LR0nI3 3NdB-

AdB(ω) =20 log(A(ω)) =20·log

K

√1+τ²·ω²

f Hw,ā3 +@aI3L<N3ATaCc

(7)

cRCj 3N 0āq3IRUUNj.

AdB(ω) =20·logK−10·log

1+τ²·ω²

H ~<na3 fY: Uaāc3Nj3 IȕIIna3 03c 0C<aLL3c 03 #R03 0ȕnN cwcjěL3 0n Ua3LC3a Ra0a3Y

10⁰ 10¹ 10² 10³

−20

−10 0 10 200#

a0gc

20·logKcwLUjRj3 @RaCyRNjI3

cwL

UjRj303 U3Nj3 A20 dB

/dec ωc= ¹_τ ²·ωc

ωc

2

A3 dB

A1 dB A1 dB

10⁰ 10¹ 10² 10³

−90

−75

−60

−45

−30

−15 0

◦

a0gc

A45ï

A63,43ï A26,56ï

7ϔόЛЁζ fY:Y Ģ /C<aLL3c 03 #R03 A cwcjěL3 0n S^3a Ra0a3 .B;`KK2 /ǶKTHBim/2 , I3 0C<aLL3 0ȕLUICjn03 Uaāc3Nj3 03nu cwLUjRj3c

ġ nN3 @RaCyRNjI3 IRac\n3ω →0- lim

ω→0(AdB) =20·logKd ġ nN3 cwLUjRj3 03 U3Nj3−20dB/decIRac\n3ω→∞d

ġ I3c cwLUjRj3c c3 ,aRCc3Nj URna I UnIcjCRN 03 ,RnUna3ωc = ¹_τd

ġ I3 0C<aLL3 cwLUjRjC\n3 3N LUICjn03 3cj cc3y UaR,@3 03 I ,Rna$3 aā3II3 3j cn|j 3N

<āNāaI URna ājn0C3a I 8RN,jCRN d

ġ URna I UnIcjCRN 03 ,RnUna3 ωc = ¹_τ .Iȕā,aj Ua aUURaj n URCNj 0ȕCNj3ac3,jCRN 03c cwLUjRj3c 3cj 03−3dBd

ġ URna I3c UnIcjCRNc 0Rn$I32·ωc3j LRCjCāωc

2 Iȕā,aj 3cj 03−1dBUa aUURaj nu cwLUA jRj3cY

.B;`KK2 /2b T?b2b , I3 0C<aLL3 03c U@c3c Uaāc3Nj3 InC nccC 03nu cwLUjRj3c ġ IRac\n3ω→^0. lim

ω→0(Φ(ω)) =0d ġ IRac\n3ω→∞. lim

ω→∞(Φ(ω)) =−^π₂rad(=−90ï)Y

ġ H3 0C<aLL3 cwLUjRjC\n3 © I 8RaL3 0ȕnN3 La,@3 0ȕ3c,IC3a. CI Nȕ3cj Uc cn|cLL3Nj Uaā,Cc URna a3Uaāc3Nj3a ,Raa3,j3L3Nj IȕāqRInjCRN 03 I U@c3Y TRna LC3nu UUaR,@3a I3 ja,ā.

CI 3cj URccC$I3 03 ja,3a I3 c3<L3Nj UccNj Ua I3c URCNjc log ₁

10τ

, 0 3j

log₁₀

τ

,−90 V3N URCNjCIIāc cna I3 <aU@3. jj3NjCRN ,3 Nȕ3cj Uc nN3 jN<3Nj3WY

ġ [n3I\n3c qI3nac UajC,nICěa3c 03 Iȕa<nL3Nj - ġ UnIcjCRN 03 ,ccna3 -Φ(ωc) =−45ï ġ UnIcjCRN LRCjCā -Φ_ω_c

2

= −arctan

τ·^ω₂^c≈ −26,56ï ġ UnIcjCRN 0Rn$I3 -Φ(2·ωc) =−arctan(τ·2·ωc)≈ −63,43ï

Hw,ā3 +@aI3L<N3ATaCc e

(8)

eX9XkX S`2KB2` Q`/`2 m MmKû`i2m`

bRCj I 8RN,jCRN 0ā~NC3 Ua I3 URIwNǃL3 0n Ua3LC3a 03<aā - N1(p) = (1+τ·p)^.

QN c3 UaRURc3 03 ,RLUa3a ,3 URIwNǃL3 © I 8RN,jCRN 03 jaNc83aj 0n Ua3LC3a Ra0a3 - H1(p) = ¹

1+τ·p.

10⁰ 10¹ 10² 10³

−30

−20

−10 0 10 20 300#

a0gc

N₁(p) =1+τ·p

H₁(p) = ¹ 1+τ·p

10⁰ 10¹ 10² 10³

−90

−60

−30 0 30 60 90

◦

a0gc

N₁(p) =1+τ·p

H₁(^p) = ¹ 1+τ·p

7ϔόЛЁζ fY9Y Ģ /C<aLL3c 03 #R03 A S^3a Ra0a3 n NnLāaj3na

ġ I3 LR0nI3 c3 0ā0nCj 0Ca3,j3L3Nj 03|N1(j·ω)|= ¹ H1(j·ω)

. cRCj 3N 0ā,C$3I

20 log(|N1(j·ω)|) =20 log 1

H1(j·ω)

= −20 log(|H1(j·ω)|)

ġ Iȕa<nL3Nj c3 0ā0nCj 03 I LćL3 LNCěa3 arg(N1(j·ω)) =arg

1 H1(j·ω)

=−arg(H1(j·ω))

QN ,RNcjj3 0RN, \n3 I3 ja,ā V~<Y fY9W 03c 0C<aLL3c 03 #R03 0ȕnN URIwNǃL3 0n Ua3LC3a Ra0a3 3cj I3 cwLājaC\n3 Ua aUURaj © Iȕu3 03c $c,Ccc3c 0n 0C<aLL3 03 #R03 0ȕnN3 8RN,jCRN 03 jaNc83aj 0n Ua3LC3a Ra0a3 VURna nN <CN nNCjCa3 F5SWY +3I 3cj <āNāaICc$I3 \n3I \n3 cRCj IȕRa0a3 03 I 8RN,jCRN 03 jaNc83ajY

4 Hw,ā3 +@aI3L<N3ATaCc

(9)

eX8X avbiĕK2 /m b2+QM/ Q`/`2

eX8XRX _TT2Hb

mN cwcjěL3 0n c3,RN0 Ra0a3 3cj 0ā,aCj Ua nN3 ā\njCRN 0C{āa3NjC3II3 ICNāCa3 © ,R3|,C3Njc ,RNcjNjc 0n c3,RN0 Ra0a3 -

1 ω²_n

d²s(t)

dt² + ²·ξ ωn

ds(t)

dt +s(t) =K.e(t) q3,

ġ K- <CN

ġ ωn- UnIcjCRN UaRUa3rad s⁻¹

ġ ξ- ,R3|,C3Nj V8,j3naW 0ȕLRajCcc3L3Nj H 8RN,jCRN 03 jaNc83aj cȕā,aCj -

H(p) = ^S(p)

E(p) = ^K p²

ω²_n +²·ξ

ωn ·p+1

eX8XkX _2T`ûb2MiiBQM 7`û[m2MiB2HH2

¨ UajCa 03 I 8RN,jCRN 03 jaNc83aj 0ȕnN c3,RN0 Ra0a3 V3\n fY9YSW RN 0āj3aLCN3 I 8RN,jCRN 03 jaNc83aj ,RLUI3u3 -

H(j·ω) = ^K 1− ^ω_ω²₂

n

+j·2·ξ·_ω^ω

n

QN 0ā0nCj -

ġ I UajC3 aā3II3 -

Re(ω) =

K

1− ^ω_ω²₂

n

1−_ω^ω²₂

n

2

+

2·ξ· _ω^ω

n

₂

ġ I UajC3 CL<CNCa3 -

Im(ω) =− ²·K·ξ·_ω^ω n

1− ^ω_ω²₂

n

2

+

2·ξ·_ω^ω

n

2

ġ I3 LR0nI3 -

A(ω) = ^K

1−_ω^ω²₂

n

2

+

2·ξ·_ω^ω

n

₂

ġ I3 LR0nI3 3NdB-

AdB(ω) =20 logK−10 log

1− ^ω_ω₂²

n

2

+

2·ξ·_ω^ω

n

₂

ġ Iȕa<nL3Nj -

Φ(ω) =−arctan

2·ξ·ω·ωn

ω_n²−ω²

Hw,ā3 +@aI3L<N3ATaCc O

(10)

MRnc qRNc qn. IRac 03 Iȕājn03 03 I aāURNc3 j3LURa3II3. \n3 IȕIIna3 03 ,3jj3 aāURNc3 0āU3N0 0n ,R3|,C3Nj 0ȕLRajCcc3L3NjξY Ājn0CRNc 0RN, 0Nc nN Ua3LC3a j3LUc I3 LR0nI3 3j IȕCNn3N,3 03 ξ cna ,3InCA,C -

bRCjA1(u). I3 LR0nI3 aā0nCj 0ā0nCj 0n LR0nI3 03 I 8RN,jCRN 03 jaNc83aj VfY9YlW. 3N URcNju= _ω^ω

n

A1(u) = ^K

(1−u²)²+ (2·ξ·u)²

+I,nIRNc I 0āaCqā3 Ua aUURaj © n dA1(u)

du =K d du

1−u²2

+ (2·ξ·u)²⁻ 1

2 =K 4·u

u²+2·ξ²−1 (1−u²)²+ (2·ξ·u)²

3 2

H3 NnLāaj3na cȕNNnI3 URna -

ġ u=0cRCjω=0,3jj3 a,CN3 ,Raa3cURN0 © nN3 cwLUjRj3 @RaCyRNjI3 0Nc I3 0C<aLL3 03 #R03 3N LUICjn03.

ġ u²+2·ξ²−1 = 0. ,3jj3 ā\njCRN Nȕ0L3j 03 a,CN3c aā3II3c \n3 URnaξ ≤

√2

2 . I a,CN3 3cj IRac ur= _ω^ω^r

n =1−2·ξ²cRCjωr= ωn·1−2·ξ²Y QN UU3II3 UnIcjCRN 03 aācRNN,3 I UnIcjCRN

ωr =ωn·1−2·ξ².

TRna ,3jj3 UnIcjCRN. I3 LR0nI3 Uaāc3Nj3 nN LuCLnL -

A(ωr) = ^K

1− ^ω_ω²^r₂

n

2

+

2·ξ·_ω^ω^r

n

₂ = ^K 2·ξ·1−ξ²

QN 0ā~NCjQr. I3 ,R3|,C3Nj 03 aācRNN,3 VRn 8,j3na 03 cnaj3NcCRNW j3I \n3 Qr = ^A(ωr)

A(ω0) = ¹ 2·ξ·1−ξ²

H3 ja,ā 0n LR0nI3 V~<Y fYfW 0ȕnN cwcjěL3 0n c3,RN0 Ra0a3 0āU3N0 0RN, 03 I qI3na 0n ,R3|,C3Nj 0ȕLRajCcc3L3NjY

ġ 0<z<

√2

2 Uaāc3N,3 0ȕnN LuCLnL URna I UnIcjCRN 03 aācRNN,3ωrd ġ

√2

2 <zUc 03 LuCLnLY

Hȕa<nL3Nj InC N3 Uaāc3Nj3 Uc 03 LuCLnL - Φ(ω) =−arctan

2·ξ·ω·ωn

ω²_n−ω²

.

BI 3cj URccC$I3 0ȕ|N3a 3N,Ra3 ,3jj3 ājn03. 3N ājn0CNj I 8RaL3 03 I 8RN,jCRN 03 jaNc83aj 3N 8RN,jCRN 03zY

QN 0CcjCN<n3 jaRCc ,c 3N 8RN,jCRN 03c a,CN3c 0n URIwNǃL3 0n 0āNRLCNj3na 03 I 8RN,jCRN 03 jaNc83aj

Sz Hw,ā3 +@aI3L<N3ATaCc

(11)

0n c3,RN0 Ra0a3 VfY9YSW -

D(p) =1+ ²·ξ·p ωn + _ω^p²₂

n =0

ġ 0 < z< 1- I3c 03nu a,CN3c 0n 0āNRLCNj3na cRNj ,RLUI3u3c ,RNEn<nā3c. I 8RN,jCRN 03 jaNc83aj N3 U3nj ćja3 cCLUIC~ā3. Iȕājn03 ājā aāICcā3 Uaā,ā03LL3Nj -

H(p) = ^S(p)

E(p) = ₁ ^K ω²_np²+²·ξ

ωn p+1

ġ z>1- I3c 03nu a,CN3c cRNj aā3II3c. I 8RN,jCRN 03 jaNc83aj IRac U3nj c3 L3jja3 cRnc I 8RaL3 0ȕnN UaR0nCj 03 03nu 8RN,jCRNc 0n Ua3LC3a Ra0a3 -

H(p) = (1+T1·p)^K·(1+T2·p) ġ LR0nI3 -

A(ω) = ^K

1+T₁²·ω²·1+T₂²·ω² ġ LR0nI3 3NdB-

AdB(ω) =20 logK−20 log(1+T₁²·ω²)−20 log(1+T₂²·ω²) ġ Iȕa<nL3Nj -

Φ(ω) =−arctan(T1·ω)−arctanT2·ω)

ġ z = 1- I3 0āNRLCNj3na URccě03 nN3 a,CN3 aā3II3 0Rn$I3. I 8RN,jCRN 03 jaNc83aj U3nj c3 L3jja3 cRnc I 8RaL3 -

H(p) = (1+^KT·p)² ġ LR0nI3 -

A(ω) = ^K 1+T²·ω² ġ LR0nI3 3NdB-

A_dB(ω) =20 logK−20 log

1+T₁²·ω² ġ a<nL3Nj -

Φ(ω) =−2·arctan(T·ω)

MRnc IIRNc 0RN, ,RNcC0āa3a URna Iȕājn03 8aā\n3NjC3II3 0n c3,RN0 Ra0a3. I3c \nja3 ,c cnCqNj -

*b 0<z<

√2

2 H 8RN,jCRN 03 jaNc83aj cȕā,aCj -H(j·ω) = ^K 1− ^ω_ω²₂

n

+j·2·ξ·_ω^ω

n

Y

¨ UajCa 0n LR0nI3 3NdB3j 03 Iȕa<nL3Nj. RN U3nj ja,3a I3c 0C<aLL3c 03 #R03 V~< fYfW. RN a3jaRnq3 cna ,3nuA,C -

/B;`KK2 /ǶKTHBim/2 ,

ġ nN3 cwLUjRj3 @RaCyRNjI3 0ȕRa0RNNā320 logKIRac\n3ω →0.

ġ nN3 cwLUjRj3 03 U3Nj3−40dB/decIRac\n3ω→+∞.

ġ I3c 03nu cwLUjRj3c c3 ,aRCc3Nj URnaω=ωnI UnIcjCRN UaRUa3.

Hw,ā3 +@aI3L<N3ATaCc SS

(12)

10⁰ 10¹ 10² 10³

−40

−30

−20

−10 0 10 20 300#

ωn a0gc

ωr

−_40dB /dec 20 logK

ξ<

√2 2

√2

2 <ξ<1 ωn

ωr

Q_0#

10⁰ 10¹ 10² 10³

−180

−150

−120

−90

−60

−30 0

◦

a0gc

ξ<

√2 2

√2

2 <ξ<1

7ϔόЛЁζ fYfY Ģ /C<aLL3c 03 #R03 l^N0 Ra0a3 A l a,CN3c ,RLUI3u3c

ġ I3 0C<aLL3 0ȕLUICjn03 Uaāc3Nj3 nN LuCLnL URna I UnIcjCRN 0Cj3 UnIcjCRN 03 aācRA NN,3ωr= ωn·1−2·ξ². q3,

Qr = |H(jωr)|

|H(0)| = ¹

2·ξ·¹−ξ².

ġ I3 LR0nI3 URna I UnIcjCRN UaRUa3 3cj -|H(jωn)|= ^K 2·ξY /B;`KK2 /2 T?b2 ,

ġ nN3 cwLUjRj3 @RaCyRNjI3 0ȕRa0RNNā30ï IRac\n3ω→0.

ġ nN3 0ȕRa0RNNā3−180ï IRac\n3ω →+∞.

ġ Φ(ωn) =arg(H(j·ωn)) =−90ïY

*b

√2

2 ≤ z < 1 QN a3jaRnq3 I3c LćL3c cwLUjRj3c \n3 0Nc I3 ,c Uaā,ā03Nj. LCc I3 0C<aLL3 0ȕLUICjn03 N3 Uaāc3Nj3 Uc 03 LuCLnL. I3 ja,ā 3cj jRnERnac cRnc I3c cwLUjRj3c 3j jaěc UaR,@3 03 ,3II3A,C VIȕā,aj 3cj n LuCLnL 03−6dBcCz=1URna I UnIcjCRNωnW 3j|H(jωn)|= ^K

2·ξ

*b z >1 HRac\n3z >1. I 8RN,jCRN 03 jaNc83aj U3nj c3 0ā,RLURc3a 3N nN UaR0nCj 03 03nu Ua3LC3ac Ra0a3c.H(p) = (1+T1·p)^K·(1+T2·p). I3 ja,ā 03c 0C<aLL3c 03 #R03 3cj 0RN, I cRLL3 <aU@C\n3 03c 03nu ja,āc 0n Ua3LC3a Ra0a3 V+8Y ~<na3 fYeWY

H3c 03nu UnIcjCRNc 03 ,ccna3 cRNjω1= ¹ T1

3jω2= ¹ T2

VURna I cnCj3 \n3ω1<ω2WY H3 0C<aLL3 0ȕLUICjn03 Uaāc3Nj3 0RN, k cwLUjRj3c -

ġ nN3 cwLUjRj3 @RaCyRNjI3 0ȕRa0RNNā320 logKIRac\n3ω →0. Vlogω → −∞W. Enc\nȕ© I UnIcjCRN ω1= ¹

T1d

Sl Hw,ā3 +@aI3L<N3ATaCc

(13)

10⁻¹ 10⁰ 10¹ 10² 10³

−50

−40

−30

−20

−10 0 10 200#

a0gc

ω1= _T¹₁ _ω_n =_T₁¹_·T₂ ω2= _T¹₂ 20 logK

−_20dB /dec

−_40dB /dec

10⁻¹ 10⁰ 10¹ 10² 10³

−180

−150

−120

−90

−60

−30 0

◦

a0gc

0ï

A90ï

A180ï

7ϔόЛЁζ fYeY Ģ /C<aLL3c 03 #R03 l^N0 Ra0a3 A l a,CN3c aā3II3c ġ nN3 cwLUjRj3 03 U3Nj3−20dB/dec3Nja3ω13jω2d

`3La\n3 - TaI3a 0ȕcwLUjRj3 3Nja3ω13jω23cj nN $nc 03 IN<<3 ,RLLnNāL3Nj 0LCc 3N njRA LjC\n3Y

H3 0C<aLL3 03c U@c3c Uaāc3Nj3 InC nccC k cwLUjRj3c -

ġ UnIcjCRN UaRUa3 -ωn=√_ω

1·ω2d

ġ Iȕa<nL3Nj URna I UnIcjCRN UaRUa3 3cj -arg(H(jωn) =−^π₂ =−90ï d ġ I3 LR0nI3 URna I UnIcjCRN UaRUa3 3cj -|H(jωn)|= ^K

2·ξ

+b z=1 H 8RN,jCRN 03 jaNc83aj 3cj nN Ua3LC3a Ra0a3 n ,aaā -H(p) = (1+^KT·p)²

H3 ja,ā 03c 0C<aLL3c 03 #R03 c3 0ā0nCj 0RN, 0Ca3,j3L3Nj 0n ja,ā 0ȕnN3 cwcjěL3 0n Ua3LC3a Ra0a3. CIc URccě03Nj 0RN, I3c UajC,nIaCjāc cnCqNj3c \n3 IȕRN a3jaRnq3 cna I ~<na3 fY4Y

ġ 0C<aLL3 0ȕLUICjn03

ġ nN3 cwLUjRj3 @RaCyRNjI3 V20 logKW IRac\n3ω → 03j nN3 cwLUjRj3 03 U3Nj3−40dB/dec V2×(−20dB/dec)W IRac\n3ω →∞d

Hw,ā3 +@aI3L<N3ATaCc Sk

(14)

10⁰ 10¹ 10² 10³

−40

−30

−20

−10 0 10 200#

a0gc

20·logK

A40 dB/dec

ωc= ¹_τ ²·ωc

2·ωc

2

A6 dB

A2 dB A2 dB

10⁰ 10¹ 10² 10³

−180

−150

−120

−90

−60

−30 0

◦

a0gc

A90ï

A126,8ï A53,1ï

7ϔόЛЁζ fY4Y Ģ /C<aLL3c 03 #R03 l^N0 Ra0a3 A S a,CN3 0Rn$I3 ġ URna I UnIcjCRN 03 ,RnUna3 ωc = ¹

T. Iȕā,aj Ua aUURaj © IȕcwLUjRj3 3cj 03 −6dB V2× (−3dB)W. Iȕā,aj Ua aUURaj nu cwLUjRj3c 3cj 03−2dBURna I3c UnIcjCRNc 0Rn$I3 3j LRCjC3 d ġ 0C<aLL3 03c U@c3c

ġ nN3 cwLUjRj3 0ȕRa0RNNā30ï IRac\n3ω→0d ġ nN3 0ȕRa0RNNā3−180ï IRac\n3ω →+∞d

ġ URnaωcIȕa<nL3Nj 03 I 8RN,jCRN 03 jaNc83aj 3cj 03−90ï d

ġ ,RLL3 URna nN cwcjěL3 0n Ua3LC3a Ra0a3 CI 3cj njCI3 03 ja,ā I3 c3<L3Nj 3Nja3 log ₁

10τ

, 0ï 3j

log₁₀

τ

,−180ï

URna LC3nu UUaR,@3a I3 ja,ā aā3IY

eXeX AMiû;`i2m`

7RN,jCRN 03 jaNc83aj - H_i(p) = ¹

Ti·p

1 T_i·p E(p) S(p)

7RN,jCRN 03 jaNc83aj ,RLUI3u3 -

Hi(jω) = ¹ T_i·j·ω ġ KR0nI3 -

|Hi(jω)|= − ¹ Ti·ω ġ KR0nI3 3N 0# -

|Hi(jω)|_dB =−20 logω−20 logTi

ġ a<nL3Nj -

arg(Hi(jω)) =−90ï

H3 0C<aLL3 0ȕLUICjn03 V~< fYOW 0ȕnN CNjā<aj3na 3cj nN3 0aRCj3 03 U3Nj3−20dB/decUccNj Ua

−20 logTiURnaω=1Vlogω=0WY

H3 0C<aLL3 03 U@c3 3cj nN3 0aRCj3 @RaCyRNjI3 0ȕRa0RNNā3−90ï Y

S: Hw,ā3 +@aI3L<N3ATaCc

(15)

10⁻¹ 10⁰ 10¹ 10²

−60

−40

−20 0 20 40 600#

a0gc

0āaCqj3na-+^20dB/dec CNjā<aj3na-−_20dB/dec

10⁻¹ 10⁰ 10¹ 10²

−90

−60

−30 0 30 60 90

◦

a0gc

0āaCqj3na

CNjā<aj3na -

7ϔόЛЁζ fYOY Ģ /C<aLL3c 03 #R03 A BNjā<aj3na A /āaCqj3na

eXdX .û`Bpi2m`

7RN,jCRN 03 jaNc83aj -

H_d(p) =T_d·p E(p) T_d·p S(p) 7RN,jCRN 03 jaNc83aj ,RLUI3u3 -

Hd(jω) =Td·j·ω ġ KR0nI3 -

|H_d(jω)|= T_d·ω ġ KR0nI3 3N 0# -

|H_d(jω)|_dB= +20 logω+20 logT_d ġ a<nL3Nj -

arg(Hd(jω)) = +90ï /C<aLL3c 03 #R03 V~< fYOW

H3 0C<aLL3 0ȕLUICjn03 0ȕnN 0āaCqj3na 3cj nN3 0aRCj3 03 U3Nj3+20dB/decUccNj Ua+20 logT_d URnaω=1Y

H3 0C<aLL3 03 U@c3 3cj nN3 0aRCj3 @RaCyRNjI3 0ȕRa0RNNā3+90ï Y

eX3X _2i`/ Tm`

bRCj nN cwcjěL3 j3I \n3 I cRajC3 3cj 3N a3ja0 cna Iȕ3Njaā3 0ȕnN j3LUcτ- s(t) =e(t−τ).

H3 j@āRaěL3 0n a3ja0 NRnc U3aL3j 0ȕā,aCa3 3N

UccNj 0Nc I3 0RLCN3 03 HUI,3 - E(p) R(p) =e⁻^τ^·^p S(p) S(p) =e⁻^τp·E(p)

H jaNc8RaLā3 03 HUI,3 0ȕnN a3ja0 Una 3cj 0RN, - R(p) =e⁻^τ^·^p

Hw,ā3 +@aI3L<N3ATaCc S9

(16)

QN 3N 0ā0nCj I 8RN,jCRN 03 jaNc83aj ,RLUI3u3 -

R(j·ω) =e⁻^τ^·^j^·^ω =R(j·ω) =cosτω−jsinτω H3 LR0nI3 3cj ,RNcjNj.

|R(j·ω|=¹ Hȕa<nL3Nj 3cj ,RNcjLL3Nj 0ā,aRCccNj V+8Y ~<na3 fYSzW

arg(R(j·ω) =−τω

eX3XRX AM~m2M+2 /ǶmM `2i`/ bm` H2 i`+û /ǶmM HB2m /2 "Q/2

TRna āqIn3a Iȕ3{3j 0ȕnN a3ja0 cna I3 IC3n 03 #R03. NRnc IIRNc ājn0C3a I 8RN,jCRN 03 jaNc83aj 0ȕnN a3ja0 Una ccR,Cā © nN Ua3LC3a Ra0a3.

H(p) =e⁻^τp 1 1+T·p.

10⁰ 10¹ 10² 10³

−40

−30

−20

−10 0 100#

a0gc

a3ja0

S^3a Ra0a3 S^3a Ra0a3 a3ja0ā

10⁰ 10¹ 10² 10³

−180

−150

−120

−90

−60

−30 0

◦

a0gc

a3ja0 S^3a Ra0a3

S^3a Ra0a3 a3ja0ā

7ϔόЛЁζ fYSzY Ģ /C<aLL3c 03 #R03 A BNn3N,3 0ȕnN a3ja0 7RN,jCRN 03 jaNc83aj ,RLUI3u3.

H(j·ω) =e⁻^τ^j^·^ω 1 1+T·j·ω ġ LR0nI3 -

|H(jω)|_dB=20 log K

1+j·τ·ω ġ a<nL3Nj -

Arg(H(jω)) =−arctan(τ·ω)−τ1·ω

QN a3La\n3 cna I ~<na3 fYSz \n3 I3 LR0nI3 Nȕ3cj Uc CNn3N,ā Ua I3 a3ja0 VI3c 03nu ja,āc cRNj cnU3aURcāW. Ua ,RNja3 Iȕa<nL3Nj 3cj 0CLCNnā 03τ·ωY

mN a3ja0 n<L3Nj3 I3 0āU@c<3 3Nja3 Iȕ3Njaā3 3j I cRajC3 0n cwcjěL3Y MRnc q3aaRNc UInc IRCN. IRac 03 Iȕājn03 03 I cj$CICjā 03c cwcjěL3c cc3aqCc. \n3 ,3j 3{3j 3cj 8Raj3L3Nj UaāEn0C,C$I3 © I cj$CICjā 03c cwcjěL3c

Sf Hw,ā3 +@aI3L<N3ATaCc

(17)

eXNX :ûMû`HBbiBQM /m i`+û /2b /B;`KK2b /2 "Q/2

iRnj3 8RN,jCRN 03 jaNc83aj cNc a3ja0 U3nj cȕā,aCa3 cRnc I 8RaL3 cnCqNj3 - H(p) = ^N(p)

D(p) = ^K p^α

1+a1·p+a2·p²+....+anpⁿ 1+b1·p+b2·p²+....+bmp^m q3,

ġ n- 03<aā 0n URIwNǃL3 0n NnLāaj3na d ġ m- 03<aā 0n URIwNǃL3 0āNRLCNj3na d ġ K- I3 <CN cjjC\n3 d

ġ α - I ,Icc3 03 I 8RN,jCRN 03 jaNc83ajY

H3 NnLāaj3na 3j I3 0āNRLCNj3na cRNj 03nu URIwNǃL3c. URna I3c cwcjěL3c U@wcC\n3c. I3 03<aā <IR$I 0n 0āNRLCNj3na 3cj cnUāaC3na n 03<aā 0n NnLāaj3na -m+α−n≥0Y

QN U3nj. 3N a3,@3a,@Nj I3c a,CN3c 03 ,@\n3 URIwNǃL3. L3jja3 I 8RN,jCRN 03 jaNc83aj cRnc I 8RaL3 cnCqNj3 -

H(p) = ^N(p) D(p) = ^K

p^α · ^∏(1+τi·p)·∏

1+2_ω^z^j

njp+_ω^p2² nj

∏(¹+τk·p)·∏

1+2_ω^z^l

nlp+_ω^p2² nl

H 8RN,jCRN 03 jaNc83aj cȕā,aCj 0RN, ,RLL3 I3 UaR0nCj 03 UIncC3nac 8RN,jCRNc āIāL3NjCa3c VUa3LC3a.

03nuCěL3 Ra0a3 3j CNjā<ajCRNg0āaCqjCRNWY H(p) = ^N(p)

D(p) =H1(p)·H2(p)·....·HI(p)·...·HN(p) +3 \nC NRnc U3aL3j 0ȕā,aCa3 I3 LR0nI3 3j Iȕa<nL3Nj 3N 0# -

KQ/mH2 2M /"

|H(j·ω)|_dB=20 log(|H1(j·ω)|) +...+20 log(|HI(j·ω)|) +...+20 log(|HN(j·ω)|)

`;mK2Mi

Arg(H(j·ω)) = Arg(H1(j·ω)) +...+Arg(HI(j·ω)) +...+Arg(HN(j·ω))

QN R$jC3Nj CNcC I3c 0C<aLL3c 03 #R03 03 I 7i 3N cRLLNj <aU@C\n3L3Nj I3c 0C<aLL3c 03

#R03 03 ,@\n3 8RN,jCRN āIāL3NjCa3Y

*QKTQ`i2K2Mi HQ`b[m2ω →∞ ġ a<nL3Nj

ġ nN3 8RN,jCRN 0n Ua3LC3a Ra0a3 UURaj3 nN 0āU@c<3 LuCLI V© IȕCN~NCW 03−90ï cC 3II3 3cj n 0āNRLCNj3na 3j 03+90ï cC 3II3 3cj n NnLāaj3na.

ġ nN3 8RN,jCRN 0n c3,RN0 Ra0a3 UURaj3 nN 0āU@c<3 LuCLI 03−180ï cC 3II3 3cj n 0āNRLCA Nj3na 3j 03+180ï cC 3II3 3cj n NnLāaj3na.

ġ nN CNjā<aj3na UURaj3 InC nN 0āU@c<3 ,RNcjNj 03−90ï 3j I3 0āaCqj3na 03+90ïY

+3c 0āU@c<3c cȕERnjNj. RN U3nj 0ā0nCa3 \n3 I3 0āU@c<3 jRjI 03 I 8RN,jCRN 03 jaNc83aj IRac\n3 I UnIcjCRN n<L3Nj3 j3N0 q3ac -

ωlim→+∞arg(H(j·ω)) = (n−m−α)·90^◦

Hw,ā3 +@aI3L<N3ATaCc Se

(18)

ġ KR0nI3

ġ I3 ja,ā 0n IC3n 03 #R03 0ȕnN Ua3LC3a Ra0a3 j3N0 q3ac nN3 cwLUjRj3 03 U3Nj3−20dB/deccȕCI 3cj 0āNRLCNj3na 3j 03+20dB/deccȕCI 3cj n NnLāaj3na.

ġ nN c3,RN0 Ra0a3 j3N0 q3ac nN3 cwLUjRj3 03 U3Nj3−40dB/deccȕCI 3cj 0āNRLCNj3na 3j 03 +40dB/deccȕCI 3cj n NnLāaj3na.

ġ I3 IC3n 03 #R03 0ȕnN CNjā<aj3na 3cj nN3 0aRCj3 03 U3Nj3−20dB/dec3j 03+20dB/decURna nN 0āaCqj3naY

+3c U3Nj3c cȕERnj3Nj. RN U3nj 0RN, 0ā0nCa3 \n3 IȕcwLUjRj3 ~NI3 nN3 U3Nj3 03 (n−m−α) 20dB/dec

*QKTQ`i2K2Mi HQ`b[m2 ω→0

¨ UajCa 03 I 8RaL3 8,jRaCcā3 03 H(p)0ā,aCj3 UInc @nj. RN 0ā0nCj \n3 IȕIIna3 03c IC3nu 03 #R03 IRac\n3ω → 0N3 0āU3N0 \n3 03 I ,Icc3α03 I 8RN,jCRN 03 jaNc83aj 3jKY 2N 3{3j. I3 LR0nI3 3NdB 3j Iȕa<nL3Nj 03 ,@\n3 8RN,jCRN 0n Ua3LC3a 3j 0n c3,RN0 Ra0a3 cRNj NnIc IRac\n3ω →0Y HȕIIna3 03c 0C<aLL3c 03 #R03 3N0c3 0ā0nCj 0RN, 03 -

ωlim→0(H(j·ω)) = lim

ω→0

K· ¹ (j·ω)^α

ġ α=0

ġ Iȕa<nL3Nj j3N0 q3ac0.

ġ I3 LR0nI3 j3N0 InC q3ac - lim

ω→0|H(j·ω)|_dB =20 logK ġ α>0

ġ Iȕa<nL3Nj j3N0 q3ac nN3 cwLUjRj3 @RaCyRNjI3 0ȕRa0RNNā3 -−α·90ï Y ġ I3 LR0nI3 j3N0 q3ac nN3 cwLUjRj3 0ȕā\njCRN -20 logK−α·²⁰·^logωY

S4 Hw,ā3 +@aI3L<N3ATaCc